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Astron. Astrophys. 324, 80-90 (1997)

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4. Discussion

The principal result of our study is that the ratio [FORMULA] of the radial scalelength h to the constant scaleheight [FORMULA] is 1.5 to 2 times higher in interacting galaxies than in isolated spiral galaxies. Moreover, the average value found [FORMULA] = 2.9, is significantly lower than all values found in the literature: Bottema (1993) found that the ratio [FORMULA] varies with total galactic luminosity, from 11 for the faintest galaxies to 5.2 for the most luminous, passing through a local minimum of 5.1 for intermediate luminosities. Both h and [FORMULA] increase steadily with luminosity, [FORMULA] by more than a factor 10. Here we found for the same galaxy types, a much lower ratio [FORMULA], which means that the tidal interaction has a strong effect in relative disk thickening.

First we can note that the effect on the ratio [FORMULA] is partly due to the absolute increase of [FORMULA] (cf figure 3), but also to the decrease of h (Fig. 6), so that the effect becomes quite significant on the ratio (Fig. 5). (The tendency for galactic disks to be shorter in strongly interacting systems was mentioned earlier in Reshetnikov et al 1993.) This means that the tidal interaction not only thickens the disk, but also strips its radial extent, or induces a concentration of the stellar disk. This is not unexpected, since it is well known that tidal interaction triggers the tranfer of angular momentum outwards, and contributes to the shrinking of the disks and concentration of the mass. This is due to strong non-axisymmetric disturbances generated in the disk by the tidal perturbation, e.g. spirals and bars. Gravity torques then produce mass inflow inside corotation, while some mass is expelled in the outer parts, and take the angular momentum away (Combes 1996). If there is a massive dark halo, it acts as a receiver of angular momentum and helps the visible mass to shrink and condense radially (Barnes 1988).

All these perturbations, thickening of the plane, and radial condensation, leading to a decrease of the ratio [FORMULA], must however be transient, and disappear after the interaction is over, i.e. on a time scale of one Gyr. Indeed, galaxies experience many interactions in a Hubble time, and those appearing isolated now, must have passed through an interaction period, may be leading to a minor merger. Present galaxies must be the result of merging of some smaller units, according to theories of bottom-up galaxy formation, where small building blocks form first, and large-scale structures virialised subsequently (e.g. Searle & Zinn 1978, Frenk et al 1988). On the observational side, many clues point to the high number of galaxy interactions: existence of shells and ripples in a significant fraction of present early-type galaxies (Schweizer & Seitzer 1988, 1992), number of presently interacting systems extrapolated to earlier times (Toomre 1977). A present day "isolated" galaxy must have experienced at least several interactions in the past, and has probably accreted several tens of percents of its mass in the form of discrete subunits (Ostriker & Tremaine 1975, Schweizer 1990). This implies that the [FORMULA] ratio recovers its high average value of 5-11 after the interaction. Since the stellar component alone cannot cool down, this means that the overall reduction of thickness should be due to gas accretion. Spiral galaxies possess HI gas reservoirs in their outer parts, that remain available for star formation. Some of this gas can be driven inwards by gravity torques due to a tidal interaction (Braine & Combes 1993). Through this increase of potential well in the plane, the stellar component can react with a slightly reduced thickness; but the main consequence will be the formation of young stars in a very thin layer. The overall thickness will be reduced, which can explain our statistical results about [FORMULA]. The signature of these interacting events are observed at the present time in terms of different stellar components in the vertical distribution of galaxies: the presence of thin and thick disks. In the Milky Way, the existence of the thick disk has been known for a long time: from in situ star counts in the direction of the south galactic pole (Gilmore & Reid 1983) and high proper motions star surveys in the solar neighborhood (Sandage & Fouts 1987). The age, metallicity and kinematics of the stars in the thick disk are intermediate between that of the thin disk and halo. From the chemical evolution, it is recognized that a substantial delay must have occurred between the formation of the thick and thin disks (e.g. Pardi et al 1995). Recently, Robin et al (1996) determined the main characteristics of the thick disk population using photometric star counts and a model of population synthesis. They found a true discontinuity between thin and thick disks, with no kinematic or abundance gradient in the thick disk, favoring the merging event hypothesis for the thickening of the disk. They claim a scaleheight of 760 pc for the thick disk, with a scalelength of 2.8 kpc, giving a [FORMULA] ratio of 3.7, still too small for a non-interacting galaxy. This might suggest that the interactions with the many dwarfs companions of our Galaxy (Ibata et al 1994) or the Magellanic Clouds have still an action on its thickness. This is even more obvious with the scaleheight parameters adopted by Reid & Majewski (1993), for whom [FORMULA] = 1.5 kpc. This view is also in agreement with recent chemical models of the Milky Way. Chiappini et al (1996) show that the recent constraints, including metallicity distribution of G-dwarf stars, impose that the disk of the Galaxy has been built at least in two main infall episodes. The halo and thick disk have formed rapidly (in a time-scale of 1 Gyr), while the thin disk is much slower to form (time-scale 8 Gyr), and the gas forming the thin disk must come from the intergalactic medium (and not from the gas shed by the halo).

As it is evident from the above discussion, one can expect a dependence between galaxy thickness and global content of HI. Fig.7 presents distributions of normal galaxies with known HI mass in the joint sample (our+vKS+BD) and of our sample interacting galaxies in the planes m(HI)/ [FORMULA] - [FORMULA] and [FORMULA] ([FORMULA] values corrected for Galactic absorption only.). There is good ([FORMULA]) inverse correlation between the HI content of a normal galaxy and its scale height (Fig.7a). Relative thickness of a galaxy - [FORMULA] - also correlates with HI content (Fig.7b). (Also, a related dependence between [FORMULA] colour and galaxy thickness is present but with less confidence.) Dashed lines in figure 7 show double regression fits for normal spirals: [FORMULA] (kpc) = 0.84 x [M(HI)/ [FORMULA] ] [FORMULA] and [FORMULA] = 5.0 x [M(HI)/ [FORMULA] ] [FORMULA], where M(HI) is the total HI mass (in [FORMULA]) and [FORMULA] is the total luminosity of the edge-on galaxy (in [FORMULA]) uncorrected for internal absorption. It is interesting that the Milky Way is also satisfying the above relations. Adopting for the absolute luminosity of "edge-on" Milky Way [FORMULA] -20.5 +1.5 = -19.0 and M(HI) = 4 109 [FORMULA], we obtain from the above correlations [FORMULA] = 1.0 [FORMULA] 0.27 kpc and [FORMULA] = 4.0 [FORMULA] 1.7. These values are in agreement with current estimates of the Milky Way parameters (e.g. Sackett 1997).

[FIGURE] Fig. 7. Distribution of normal (circles) and interacting (solid triangles) galaxies in the plane HI mass-to-blue luminosity ratio - scale height (a) and HI mass-to-blue luminosity ratio - [FORMULA] (b).

Interacting galaxies in general follow the same relations as normal galaxies but with larger scatter. Existence of this correlation can be attributed to the dissipative character of the gas: after a perturbation event that heats both the stellar and gas disks, the gas can dissipate the extra-kinetic energy away, and flatten again to its regulated thin disk. Regulation is probably due to gravitational instabilities, as developed by Lin & Pringle (1987): instabilities heats the medium until Toomre Q parameter is high enough to suppress gravitational instabilities. The gas then cools down until instabilities enter again the process. This feed-back mechanism could explain why the observed gas velocity dispersion is constant with radius (e.g. Dickey et al 1990). In very gas rich galaxies, after a galaxy interaction that has heated the stellar disk, gas dissipation can quickly makes the galaxy recover its equilibrium thickness, through star formation in the thin gas disk. The mass ratio between the thick and thin stellar disk depends strongly on the gas content, and will determine the final global disk thickness. Note that this correlation is also related to that found by Bottema (1993) as a function of mass. Fainter objects correspond to late-type galaxies which are proportionally more gas-rich, and show the higher [FORMULA] ratios.

It is interesting to compare our observational results to the predictions of N-body simulations. Quinn et al (1993) have addressed the specific problem of disk heating by small satellites, through stellar tree-code calculations. They found that the disk heats vertically as well as radially; however the radial spread is accompanied by a central mass concentration and the inner disk scalelength h decreases, while the central brightness increases, and the scaleheight [FORMULA] increases during an interaction. This corresponds quite well to our observations of a lower [FORMULA] ratio for interacting galaxies. Quantitatively, they found in average a decrease of h by 20%, while [FORMULA] increases by a factor 2. Their simulations however over-estimate the disk heating, since their dark matter halo is rigid, and cannot acquire energy and angular momentum, and they ignore the gaseous component, that can dissipate away the energy through radiation. They show that the internal heating of the primary disk depends strongly on the mass concentration of the satellite: when the latter is denser than the primary, it is not disrupted until the final merging, while when the satellite is more diffuse, it is stripped all along the interaction, and the stripped particles can take the heating away. In this case, about 95% of the disk heating must occur in the vertical direction, since the planar kinetic energy resides in the stripped stars of the satellite. Indirect effects can then modify somewhat this picture: if a strong spiral structure is triggered in the disk, this gravitational instability heats the disk, which spreads out as the angular momentum is transferred outwards. The final result depends however on the amount of gas present, and the Quinn et al (1993) simulations did not include it.

Quinn et al (1993) predicted that the final scale height [FORMULA] should increase with radius, i.e. the thickened disk should flare. This is not generally seen in our observations; only the double system VV 490 reveals a strong flare (by 50%); but the phenomenon in the simulations is significant only after 10 kpc in radius, and our observations are not sensitive enough at large radii. Shaw & Gilmore (1989, 1990) also found a constant scaleheight for their sample of isolated undistrubed edge-on galaxies. This does not seem to support the numerical predictions, since long after an interaction, the flaring is expected to subsist in the thick disk. Only in rare cases the stellar disk reveals a flaring (e.g. NGC 3115, Cappacioli et al 1988).

The simulations by Walker et al (1996) improved over the first work by Quinn et al (1993) in treating the dark haloes consistently, and dealing with an order of magnitude more particles. However the results are quite similar, they found a decrease of the scalelength of the inner disk h of about 15%, while the envelope in the outer parts was enriched through radial spreading of the primary disk. The thickness of the disk increased by 60% at the solar distance from the center. This figures imply a disk heating only slightly inferior to what was found by Quinn et al (1993), and completely within the variations expected from the nature of the satellite (dense or diffuse). They also ignored the gas component, which could bring more qualitative differences. Hernquist & Mihos (1995) simulated minor mergers between gas-rich disks and less massive dwarf galaxies. The large difference they found with comparable simulations without gas, is the huge central mass concentration driven by tidal torques due to tidally-induced bars on the gas. Half of the gas mass is driven to a region less than 1 kpc across, and triggers a starburst there. Consequent to the central mass concentration, the inner scalelength of the disk decreases, while the disk thickens. Unfortunately, star-formation was not included in these simulations, which might over-estimate the gas inflow.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998